ii
Assistant Editor: Laura Cheu
Editorial Assistant: Royden Tonomura
Senior Production Editor: Teri Hyde
Marketing Manager: Rob Merino
Manufacturing Supervisor: Janet Weaver
Art and Design Manager: Kevin Berry
Cover Design: Yvo Riezebos (technical drawing by K. Passino)
Text Design: Peter Vacek
Design Macro Writer: William Erik Baxter
Copyeditor: Brian Jones
Proofreader: Holly McLean-Aldis
Copyright c 1998 Addison Wesley Longman, Inc.
All rights reserved. No part of this publication may be reproduced, or stored in a database
or retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of the pub-
lisher. Printed in the United States of America. Printed simultaneously in Canada.
Many of the designations used by manufacturers and sellers to distinguish their products
are claimed as trademarks. Where those designations appear in this book, and Addison-
Wesley was aware of a trademark claim, the designations have been printed in initial caps
or in all caps.
MATLAB is a registered trademark of The MathWorks, Inc.
Library of Congress Cataloging-in-Publication Data
Passino, Kevin M.
Fuzzy control / Kevin M. Passino and Stephen Yurkovich.
p. cm.
Includes bibliographical references and index.
ISBN 0-201-18074-X
1. Automatic control. 2. Control theory. 3. Fuzzy systems.
I. Yurkovich, Stephen. II. Title.
TJ213.P317 1997 97-14003
629.8’9--DC21 CIP
Instructional Material Disclaimer: The programs presented in this book have been
included for their instructional value. They have been tested with care but are not guaran-
teed for any particular purpose. Neither the publisher or the authors oﬀer any warranties
or representations, nor do they accept any liabilities with respect to the programs.
About the Cover: An explanation of the technical drawing is given in Chapter 2 on
page 50.
ISBN 0–201–18074–X
1 2 3 4 5 6 7 8 9 10—CRW—01 00 99 98 97

Preface
Fuzzy control is a practical alternative for a variety of challenging control applica-
tions since it provides a convenient method for constructing nonlinear controllers
via the use of heuristic information. Such heuristic information may come from
an operator who has acted as a “human-in-the-loop” controller for a process. In
the fuzzy control design methodology, we ask this operator to write down a set of
rules on how to control the process, then we incorporate these into a fuzzy con-
troller that emulates the decision-making process of the human. In other cases, the
heuristic information may come from a control engineer who has performed exten-
sive mathematical modeling, analysis, and development of control algorithms for a
particular process. Again, such expertise is loaded into the fuzzy controller to au-
tomate the reasoning processes and actions of the expert. Regardless of where the
heuristic control knowledge comes from, fuzzy control provides a user-friendly for-
malism for representing and implementing the ideas we have about how to achieve
high-performance control.
In this book we provide a control-engineering perspective on fuzzy control.
We are concerned with both the construction of nonlinear controllers for challeng-
ing real-world applications and with gaining a fundamental understanding of the
dynamics of fuzzy control systems so that we can mathematically verify their prop-
erties (e.g., stability) before implementation. We emphasize engineering evaluations
of performance and comparative analysis with conventional control methods. We
introduce adaptive methods for identiﬁcation, estimation, and control. We exam-
ine numerous examples, applications, and design and implementation case studies
throughout the text. Moreover, we provide introductions to neural networks, ge-
netic algorithms, expert and planning systems, and intelligent autonomous control,
and explain how these topics relate to fuzzy control.
Overall, we take a pragmatic engineering approach to the design, analysis,
performance evaluation, and implementation of fuzzy control systems. We are not
concerned with whether the fuzzy controller is “artiﬁcially intelligent” or with in-
vestigating the mathematics of fuzzy sets (although some of the exercises do), but
vii

viii
rather with whether the fuzzy control methodology can help solve challenging real-
world problems.
Overview of the Book
The book is basically broken into three parts. In Chapters 1–4 we cover the basics of
“direct” fuzzy control (i.e., the nonadaptive case). In Chapters 5–7 we cover adap-
tive fuzzy systems for estimation, identiﬁcation, and control. Finally, in Chapter 8
we brieﬂy cover the main areas of intelligent control and highlight how the topics
covered in this book relate to these areas. Overall, we largely focus on what one
could call the “heuristic approach to fuzzy control” as opposed to the more recent
mathematical focus on fuzzy control where stability analysis is a major theme.
In Chapter 1 we provide an overview of the general methodology for conven-
tional control system design. Then we summarize the fuzzy control system design
process and contrast the two. Next, we explain what this book is about via a simple
motivating example. In Chapter 2 we ﬁrst provide a tutorial introduction to fuzzy
control via a two-input, one-output fuzzy control design example. Following this
we introduce a general mathematical characterization of fuzzy systems and study
their fundamental properties. We use a simple inverted pendulum example to illus-
trate some of the most widely used approaches to fuzzy control system design. We
explain how to write a computer program to simulate a fuzzy control system, using
either a high-level language or Matlab1 . In the web and ftp pages for the book we
provide such code in C and Matlab. In Chapter 3 we use several case studies to
show how to design, simulate, and implement a variety of fuzzy control systems.
In these case studies we pay particular attention to comparative analysis with con-
ventional approaches. In Chapter 4 we show how to perform stability analysis of
fuzzy control systems using Lyapunov methods and frequency domain–based sta-
bility criteria. We introduce nonlinear analysis methods that can be used to predict
and eliminate steady-state tracking error and limit cycles. We then show how to
use the analysis approaches in fuzzy control system design. The overall focus for
these nonlinear analysis methods is on understanding fundamental problems that
can be encountered in the design of fuzzy control systems and how to avoid them.
In Chapter 5 we introduce the basic “function approximation problem” and
show how identiﬁcation, estimation, prediction, and some control design problems
are a special case of it. We show how to incorporate heuristic information into the
function approximator. We show how to form rules for fuzzy systems from data pairs
and show how to train fuzzy systems from input-output data with least squares,
gradient, and clustering methods. And we show how one clustering method from
fuzzy pattern recognition can be used in conjunction with least squares methods to
construct a fuzzy model from input-output data. Moreover, we discuss hybrid ap-
proaches that involve a combination of two or more of these methods. In Chapter 6
we introduce adaptive fuzzy control. First, we introduce several methods for auto-
matically synthesizing and tuning a fuzzy controller, and then we illustrate their
application via several design and implementation case studies. We also show how
1. MATLAB is a registered trademark of The MathWorks, Inc.

ix
to tune a fuzzy model of the plant and use the parameters of such a model in the
on-line design of a controller. In Chapter 7 we introduce fuzzy supervisory control.
We explain how fuzzy systems can be used to automatically tune proportional-
integral-derivative (PID) controllers, how fuzzy systems provide a methodology
for constructing and implementing gain schedulers, and how fuzzy systems can be
used to coordinate the application and tuning of conventional controllers. Follow-
ing this, we show how fuzzy systems can be used to tune direct and adaptive fuzzy
controllers. We provide case studies in the design and implementation of fuzzy
supervisory control.
In Chapter 8 we summarize our control engineering perspective on fuzzy control,
provide an overview of the other areas of the ﬁeld of “intelligent control,” and
explain how these other areas relate to fuzzy control. In particular, we brieﬂy cover
neural networks, genetic algorithms, knowledge-based control (expert systems and
planning systems), and hierarchical intelligent autonomous control.
Examples, Applications, and Design and Implementation Case Studies
We provide several design and implementation case studies for a variety of appli-
cations, and many examples are used throughout the text. The basic goals of these
case studies and examples are as follows:
• To help illustrate the theory.
• To show how to apply the techniques.
• To help illustrate design procedures in a concrete way.
• To show what practical issues are encountered in the development and implemen-
tation of a fuzzy control system.
Some of the more detailed applications that are studied in the chapters and their
accompanying homework problems are the following:
• Direct fuzzy control: Translational inverted pendulum, fuzzy decision-making sys-
tems, two-link ﬂexible robot, rotational inverted pendulum, and machine schedul-
ing (Chapters 2 and 3 homework problems: translational inverted pendulum, au-
tomobile cruise control, magnetic ball suspension system, automated highway sys-
tem, single-link ﬂexible robot, rotational inverted pendulum, machine scheduling,
motor control, cargo ship steering, base braking control system, rocket velocity
control, acrobot, and fuzzy decision-making systems).
• Nonlinear analysis: Inverted pendulum, temperature control, hydrofoil controller,
underwater vehicle control, and tape drive servo (Chapter 4 homework problems:
inverted pendulum, magnetic ball suspension system, temperature control, and
hydrofoil controller design).

x
• Fuzzy identiﬁcation and estimation: Engine intake manifold failure estimation,
and failure detection and identiﬁcation for internal combustion engine calibra-
tion faults (Chapter 5 homework problems: tank identiﬁcation, engine friction
estimation, and cargo ship failures estimation).
• Adaptive fuzzy control: Two-link ﬂexible robot, cargo ship steering, fault toler-
ant aircraft control, magnetically levitated ball, rotational inverted pendulum,
machine scheduling, and level control in a tank (Chapter 6 homework problems:
tanker and cargo ship steering, liquid level control in a tank, rocket velocity con-
trol, base braking control system, magnetic ball suspension system, rotational
inverted pendulum, and machine scheduling).
• Supervisory fuzzy control: Two-link ﬂexible robot, and fault-tolerant aircraft con-
trol (Chapter 7 homework problems: liquid level control, and cargo and tanker
ship steering).
Some of the applications and examples are dedicated to illustrating one idea from
the theory or one technique. Others are used in several places throughout the text
to show how techniques build on one another and compare to each other. Many of
the applications show how fuzzy control techniques compare to conventional control
methodologies.
World Wide Web Site and FTP Site: Computer Code Available
The following information is available electronically:
• Various versions of C and Matlab code for simulation of fuzzy controllers, fuzzy
control systems, adaptive fuzzy identiﬁcation and estimation methods, and adap-
tive fuzzy control systems (e.g., for some examples and homework problems in
the text).
• Other special notes of interest, including an errata sheet if necessary.
You can access this information via the web site:
http://www.awl.com/cseng/titles/0-201-18074-X
or you can access the information directly via anonymous ftp to
ftp://ftp.aw.com/cseng/authors/passino/fc
For anonymous ftp, log into the above machine with a username “anonymous” and
use your e-mail address as a password.
Organization, Prerequisites, and Usage
Each chapter includes an overview, a summary, and a section “For Further Study”
that explains how the reader can continue study in the topical area of the chapter.
At the end of each chapter overview, we explain how the chapter is related to the

xi
others. This includes an outline of what must be covered to be able to understand
the later chapters and what may be skipped on a ﬁrst reading. The summaries at
the end of each chapter provide a list of all major topics covered in that chapter so
that it is clear what should be learned in each chapter.
Each chapter also includes a set of exercises or design problems and often both.
Exercises or design problems that are particularly challenging (considering how far
along you are in the text) or that require you to help deﬁne part of the problem are
designated with a star (“ ”) after the title of the problem. In addition to helping
to solidify the concepts discussed in the chapters, the problems at the ends of
the chapters are sometimes used to introduce new topics. We require the use of
computer-aided design (CAD) for fuzzy controllers in many of the design problems
at the ends of the chapters (e.g., via the use of Matlab or some high-level language).
The necessary background for the book includes courses on diﬀerential equa-
tions and classical control (root locus, Bode plots, Nyquist theory, lead-lag com-
pensation, and state feedback concepts including linear quadratic regulator design).
Courses on nonlinear stability theory and adaptive control would be helpful but
are not necessary. Hence, much of the material can be covered in an undergraduate
course. For instance, one could easily cover Chapters 1–3 in an undergraduate course
as they require very little background besides a basic understanding of signals and
systems including Laplace and z-transform theory (one application in Chapter 3
does, however, require a cursory knowledge of the linear quadratic regulator). Also,
many parts of Chapters 5–7 can be covered once a student has taken a ﬁrst course
in control (a course in nonlinear control would be helpful for Chapter 4 but is not
necessary). One could cover the basics of fuzzy control by adding parts of Chapter 2
to the end of a standard undergraduate or graduate course on control. Basically,
however, we view the book as appropriate for a ﬁrst-level graduate course in fuzzy
control.
We have used the book for a portion (six weeks) of a graduate-level course on
intelligent control and for undergraduate independent studies and design projects.
In addition, portions of the text have been used for short courses and workshops on
fuzzy control where the focus has been directed at practicing engineers in industry.
Alternatively, the text could be used for a course on intelligent control. In this
case, the instructor could cover the material in Chapter 8 on neural networks and
genetic algorithms after Chapter 2 or 3, then explain their role in the topics covered
in Chapters 5, 6, and 7 while these chapters are covered. For instance, in Chapter 5
the instructor would explain how gradient and least squares methods can be used
to train neural networks. In Chapter 6 the instructor could draw analogies between
neural control via the radial basis function neural network and the fuzzy model
reference learning controller. Also, for indirect adaptive control, the instructor could
explain how, for instance, the multilayer perceptron or radial basis function neural
networks can be used as the nonlinearity that is trained to act like the plant. In
Chapter 7 the instructor could explain how neural networks can be trained to serve
as gain schedulers. After Chapter 7 the instructor could then cover the material on
expert control, planning systems, and intelligent autonomous control in Chapter 8.
Many more details on strategies for teaching the material in a fuzzy or intelligent

xii
control course are given in the instructor’s manual, which is described below.
Engineers and scientists working in industry will ﬁnd that the book will serve
nicely as a “handbook” for the development of fuzzy control systems, and that the
design, simulation, and implementation case studies will provide very good insights
into how to construct fuzzy controllers for speciﬁc applications. Researchers in
academia and elsewhere will ﬁnd that this book will provide an up-to-date view
of the ﬁeld, show the major approaches, provide good references for further study,
and provide a nice outlook for thinking about future research directions.
Instructor’s Manual
An Instructor’s Manual to accompany this textbook is available (to instructors only)
from Addison Wesley Longman. The Instructor’s Manual contains the following:
• Strategies for teaching the material.
• Solutions to end-of-chapter exercises and design problems.
• A description of a laboratory course that has been taught several times at The
Ohio State University which can be run in parallel with a lecture course that is
taught out of this book.
• An electronic appendix containing the computer code (e.g., C and Matlab code)
for solving many exercises and design problems.
Sales Specialists at Addison Wesley Longman will make the instructor’s manual
available to qualiﬁed instructors. To ﬁnd out who your Addison Wesley Longman
Sales Specialist is please see the web site:
http://www.aw.com/cseng/
or send an email to:
cseng@aw.com
Feedback on the Book
It is our hope that we will get the opportunity to correct any errors in this book;
hence, we encourage you to provide a precise description of any errors you may
ﬁnd. We are also open to your suggestions on how to improve the textbook. For
this, please use either e-mail (passino@ee.eng.ohio-state.edu) or regular mail to the
ﬁrst author: Kevin M. Passino, Dept. of Electrical Engineering, The Ohio State
University, 2015 Neil Ave., Columbus, OH 43210-1272.
Acknowledgments
No book is written in a vacuum, and this is especially true for this one. We must
emphasize that portions of the book appeared in earlier forms as conference pa-
pers, journal papers, theses, or project reports with our students here at Ohio

xiii
State. Due to this fact, these parts of the text are sometimes a combination of our
words and those of our students (which are very diﬃcult to separate at times).
In every case where we use such material, the individuals have given us permis-
sion to use it, and we provide the reader with a reference to the original source
since this will typically provide more details than what are covered here. While
we always make it clear where the material is taken from, it is our pleasure to
highlight these students’ contributions here as well. In particular, we drew heavily
from work with the following students and papers written with them (in alpha-
betical order): Anthony Angsana [4], Scott C. Brown [27], David L. Jenkins [83],
Waihon Andrew Kwong [103, 104, 144], Eric G. Laukonen [107, 104], Jeﬀrey R.
Layne [110, 113, 112, 114, 111], William K. Lennon [118], Sashonda R. Morris
[143], Vivek G. Moudgal [145, 144], Jeﬀrey T. Spooner [200, 196], and Moeljono
Widjaja [235, 244]. These students, and Mehmet Akar, Mustafa K. Guven, Min-
Hsiung Hung, Brian Klinehoﬀer, Duane Marhefka, Matt Moore, Hazem Nounou,
Jeﬀ Palte, and Jerry Troyer helped by providing solutions to several of the exer-
cises and design problems and these are contained in the instructor’s manual for this
book. Manfredi Maggiore helped by proofreading the manuscript. Scott C. Brown
and Ra´l Ord´nez assisted in the development of the associated laboratory course
u o˜
at OSU.
We would like to gratefully acknowledge the following publishers for giving us
permission to use ﬁgures that appeared in some of our past publications: The In-
stitute of Electrical and Electronic Engineers (IEEE), John Wiley and Sons, Hemi-
sphere Publishing Corp., and Kluwer Academic Publishers. In each case where we
use a ﬁgure from a past publication, we give the full reference to the original pa-
per, and indicate in the caption of the ﬁgure that the copyright belongs to the
appropriate publisher (via, e.g., “ c IEEE”).
We have beneﬁted from many technical discussions with many colleagues who
work in conventional and intelligent control (too many to list here); most of these
persons are mentioned by referencing their work in the bibliography at the end of
the book. We would, however, especially like to thank Zhiqiang Gao and Oscar R.
Gonz´lez for class-testing this book. Moreover, thanks go to the following persons
a
who reviewed various earlier versions of the manuscript: D. Aaronson, M.A. Abidi,
S.P. Colombano, Z. Gao, O. Gonz´lez, A.S. Hodel, R. Langari, M.S. Stachowicz,
a
and G. Vachtsevanos.
We would like to acknowledge the ﬁnancial support of National Science Foun-
dation grants IRI-9210332 and EEC-9315257, the second of which was for the de-
velopment of a course and laboratory for intelligent control. Moreover, we had
additional ﬁnancial support from a variety of other sponsors during the course of
the development of this textbook, some of whom gave us the opportunity to apply
some of the methods in this text to challenging real-world applications, and others
where one or both of us gave a course on the topics covered in this book. These
sponsors include Air Products and Chemicals Inc., Amoco Research Center, Bat-
telle Memorial Institute, Delphi Chassis Division of General Motors, Ford Motor
Company, General Electric Aircraft Engines, The Center for Automotive Research
(CAR) at The Ohio State University, The Center for Intelligent Transportation

xiv
Research (CITR) at The Ohio State University, and The Ohio Aerospace Institute
(in a teamed arrangement with Rockwell International Science Center and Wright
Laboratories).
We would like to thank Tim Cox, Laura Cheu, Royden Tonomura, Teri Hyde,
Rob Merino, Janet Weaver, Kevin Berry, Yvo Riezebos, Peter Vacek, William Erik
Baxter, Brian Jones, and Holly McLean-Aldis for all their help in the production
and editing of this book. Finally, we would most like to thank our wives, who have
helped set up wonderful supportive home environments that we value immensely.
Kevin Passino
Steve Yurkovich
Columbus, Ohio
July 1997